def saastamoinen_zenith_wet_delay(latitude, height, temperature, e):
r"""Calculates zenith wet delay based Saastamoinen model
The total tropospheric delay for a given zenith distance :math:`z` is determined after Equation (19a) in
Saastamoinen :cite:`saastamoinen1972`:
.. math::
\Delta T = 0.002277 \cdot \sec z \cdot (p + (1255/T + 0.05) \cdot e) - 1.16 \cdot \tan^2 z
The zenith tropospheric delay is determined with :math:`z = 0`:
.. math::
\Delta T^z = \Delta T_h^z + \Delta T_w^z = zhd + zwd
with the zenith hydrostatic delay :math:`zhd = 0.002277 \cdot p` and zenith wet delay
:math:`zwd = 0.002277 \cdot (1255/T + 0.05) \cdot e`.
Args:
latitude (numpy.ndarray): Geodetic latitude for each observation in [rad]
height (numpy.ndarray): Orthometric height for each observation in [m]
temperature (numpy.ndarray): Temperature for each observation in [Celsius]
e (numpy.ndarray): Water vapor pressure for each observation in [hPa]
Returns:
numpy.ndarray: Zenith wet delay for each observation in [m]
"""
# Zenith wet delay based on Eq. (19a) in Saastamoinen :cite:`saastamoinen1972`
return 0.002_276_8 * (1255 / Unit.celsius_to_kelvin(temperature) +
0.05) * e
def davis_zenith_wet_delay(latitude, height, temperature, e):
r"""Calculates zenith wet delay based on Saastamoinen/Davis model
The total tropospheric delay for a given zenith distance :math:`z` is determined after Equation (19a) in
Saastamoinen :cite:`saastamoinen1972`:
.. math::
\Delta T = 0.002277 \cdot \sec z \cdot (p + (1255/T + 0.05) \cdot e) - 1.16 \cdot \tan^2 z
The zenith tropospheric delay is determined with :math:`z = 0`:
.. math::
\Delta T^z = \Delta T_h^z + \Delta T_w^z = zhd + zwd
with the zenith hydrostatic delay :math:`zhd = 0.002277 \cdot p` and zenith wet delay :math:`zwd = 0.002277 \cdot
(1255/T + 0.05) \cdot e`.
A Fortran routine written by Davis corrects also for the gravity effect due to height :math:`H` and latitude
:math:`\phi` (see http://acc.igs.org/tropo/wetsaas.f) and uses the constant :math:`0.0022768` instead of
:math:`0.002277`, which leads to
.. math::
zwd = 0.0022768 \cdot (1255/T + 0.05) \cdot e / (1 - 0.00266 \cos 2 \phi - 0.00000028 H) .
The difference between the orthometric height and geodetic height is called geoid undulation and can reach up to
100 m due to Boehm et al. :cite:`boehm2007`. The influence of height difference is not significant in this
equation. The geodetic (ellipsoidal) height is therefore often used instead of the orthometric height.
Args:
latitude (numpy.ndarray): Geodetic latitude for each observation in [rad]
height (numpy.ndarray): Orthometric height for each observation in [m]
temperature (numpy.ndarray): Temperature for each observation in [Celsius]
e (numpy.ndarray): Water vapor pressure for each observation in [hPa]
Returns:
numpy.ndarray: Zenith wet delay for each observation in [m]
"""
gravity_corr = saastamoinen_gravity_correction(latitude, height)
# Zenith wet delay based on Eq. (19a) in Saastamoinen :cite:`saastamoinen1972` with additional gravity
# correction
zwd = 0.002_276_8 * (1255 / Unit.celsius_to_kelvin(temperature) +
0.05) * e / gravity_corr
return zwd
